Sequences & series worksheet with answers

Free printable Sequences & series worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
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Find the sum S18 of the first 18 terms of the arithmetic sequence −12, −9.5, −7, −4.5, …

a₁ = −12d = 2.5n = 18
S18 =
2.Easy
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Find the sum S15 of the first 15 terms of the arithmetic sequence 12, 12.5, 13, 13.5, …

a₁ = 12d = 0.5n = 15
S15 =
3.Medium
xx₀ = 0??R

Find the radius of convergence R of the power series Σk=1∞ (1/2)ᵏ·xᵏ/(k + 1).

Σ (1/2)ᵏ·xᵏ/(k + 1)x₀ = 0
R =
4.Medium
AΣ (5/4)ᵏk = 1 … ∞BΣ (1/3)ᵏk = 1 … ∞CΣ k!/10ᵏk = 1 … ∞DΣ (1 + 1/k)ᵏk = 1 … ∞

Exactly one of the four series converges. Click it.

A: Σ (5/4)ᵏB: Σ (1/3)ᵏC: Σ k!/10ᵏD: Σ (1 + 1/k)ᵏ
  1. 1A: Σ (5/4)ᵏ
  2. 2B: Σ (1/3)ᵏ
  3. 3C: Σ k!/10ᵏ
  4. 4D: Σ (1 + 1/k)ᵏ
5.Hard

f(x) = sin x is approximated by its Maclaurin polynomial of degree 3 at x = 0.3. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = 1 to find the largest possible error |R₃|.

f(x) = sin xn = 3x = 0.3M = 1
|R₃| =
6.Hard

f(x) = cos x is approximated by its Maclaurin polynomial of degree 5 at x = 0.8. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = 1 to find the largest possible error |R₅|.

f(x) = cos xn = 5x = 0.8M = 1
|R₅| =

Answer key

  1. 1. S18 = 166.5
  2. 2. S15 = 232.5
  3. 3. R = 2
  4. 4. B: Σ (1/3)ᵏ
  5. 5. |R₃| = 0.0003375
  6. 6. |R₅| = 0.0003641

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